Asymptotic Behavior For Parabolic-Elliptic Keller-Segel Chemotaxis System With Logistic Source

This paper deals with a parabolic-elliptic chemotaxis system with nonlinear sensitivity and logistic source under homogeneous Neumann boundary conditions, in a smooth bounded domain Ω (?)Rn (n≥ 1). The functions (ψ/(s), g(s), f(s)) ∈ C1+α ([0,∞)) × C1+α ([0, ∞)) × C0 ([0, ∞)) ∩ C1 ((0, oo)) satisfy the following assumptions and respectively. We prove that for any M0> 0 if ||u0||L∞≤M0, b large enough and q,k,l satisfy some addition conditions, then the solution (u, v) converges to the positive constant equilibrium (?).